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Machine Element / Plastic Design

Cantilever Snap-Fit Design Simulator

Quick answer
For a cantilever snap-fit, the insertion force is P=3EIy/L³ (I=bh³/12) and the maximum strain is ε=1.5·h·y/L². Keeping this ε below the material's allowable strain prevents the hook from cracking.

Design the snap-fit hooks that make plastic parts click together. Adjust the beam length, root thickness and undercut to see the peak assembly strain and insertion force update in real time, and find a hook shape that won't crack.

Parameters
Resin material
Sets Young's modulus E and allowable strain ε_perm
Beam length L
mm
Root thickness h
mm
Beam width b
mm
Undercut y
mm
Deflection the hook must clear during assembly
Friction coefficient μ
Insertion lead angle α
°
Slope angle of the lead-in face of the hook
Return (retention) angle α'
°
Angle of the return face. 90° = inseparable
Results
—
Max strain ε (%)
—
Allow. undercut y_perm (mm)
—
Strain safety ε_perm/ε
—
Deflection force P (N)
—
Insertion force W (N)
—
Removal force W' (N)
—
Snap-fit cross-section — insertion animation

The hook deflects up to the undercut y during assembly and snaps back once it clears the mating part. Colour shows the strain level (green → orange → red).

Insertion force profile W(stroke)
Design sensitivity — max strain ε vs beam length L
Theory & Key Formulas

$$\varepsilon = \frac{3\,h\,y}{2\,L^{2}}, \qquad y_{\text{perm}} = \frac{2\,\varepsilon_{\text{perm}}\,L^{2}}{3\,h}$$

Maximum strain ε at the root and the allowable undercut y_perm. h: root thickness, L: beam length, y: undercut. Strain scales with thickness and inversely with the square of length.

$$P = \frac{3\,E\,I\,y}{L^{3}}, \qquad I = \frac{b\,h^{3}}{12}$$

Deflection force P (the force to bend the hook to the undercut y). E: Young's modulus, I: second moment of area, b: width.

$$W = P\cdot\frac{\mu+\tan\alpha}{1-\mu\tan\alpha}, \qquad W' = P\cdot\frac{\mu+\tan\alpha'}{1-\mu\tan\alpha'}$$

Insertion force W and removal force W'. μ: friction coefficient, α: insertion lead angle, α': return angle. When the denominator reaches zero or below, the joint becomes self-locking (permanent).

What is the Cantilever Snap-Fit Design Simulator?

🙋
A "snap-fit" is when a plastic part clicks into place, right? Why can it bend over and over without breaking?
🎓
Exactly — the kind you see on a remote-control battery cover or around a bottle cap. The mechanism is simple: it is just a cantilever beam with a "hook" at the tip. During assembly the hook has to bend a lot for a moment to clear the mating part. As long as the strain produced at the root stays below the material's limit, it springs right back. Go over the limit and it stress-whitens or snaps on the very first try.
🙋
So a bigger undercut should hold better — but I guess it's not that simple? When I raise the "undercut y" on the left, the strain turns red fast.
🎓
Good catch. A larger undercut y means bending the beam deeper, so the root strain ε = 3hy/(2L²) shoots up. That is why there is an upper limit, the "allowable undercut y_perm". A classic field failure happens here: a prototype is fine after one or two assemblies, but once a customer engages a mass-produced part dozens of times, an over-strained hook fatigues and breaks. So keep y at about 70-80% of y_perm.
🙋
If I can't be greedy with the undercut, what do I change to lower the strain?
🎓
The most effective move is to make the beam longer. Strain is inversely proportional to the square of length L, so making L 1.4× longer almost halves the strain. Move the slider on the "Design sensitivity" chart below and you will see that steep curve. The next lever is a thinner root — but too thin and the retention force drops. For a car interior panel, for example, engineers use long, thin, low-strain beams and make up the total holding force with the number of hooks.
🙋
It's interesting that insertion force and removal force come out separately. Why split them?
🎓
To tune "easy to assemble" and "hard to remove" independently for each use. A smaller insertion lead angle α makes assembly easier. A larger return angle α' makes it harder to pull apart, and beyond a certain angle the denominator drops to zero or below, giving a "self-locking — never comes off" design. A battery cover you open often gets a modest α'; an internal housing clip that may stay permanent gets α' = 90°.

Frequently Asked Questions

For a cantilever beam of constant rectangular section, the maximum strain at the root for a tip deflection y is ε = 3hy / (2L²), where h is the root thickness and L is the beam length. Strain is proportional to thickness h and inversely proportional to the square of length L, so the basic rule for bending a hook far without breaking it is to make the beam thinner and longer. This tool compares ε with the material's allowable strain and shows the safety factor.
The allowable undercut is y_perm = 2·ε_perm·L² / (3h). ε_perm is the allowable strain for a single assembly — roughly 2% for ABS and 6% for POM. For L=20mm, h=2mm and ε_perm=2%, y_perm ≈ 2.7mm. Exceeding it causes yielding, stress-whitening or cracking at the root during assembly. In practice, keep the undercut to about 70-80% of the calculated y_perm.
Insertion force W is proportional to the deflection force P: W = P·(μ+tanα)/(1−μ·tanα). Three ways to lower it: (1) reduce the lead angle α (around 30° is typical), (2) reduce friction μ at the contact face (mold release, surface finish), and (3) make the beam longer and thinner to cut P itself. Note that reducing P too far also weakens the retention, so balance insertion force against retention force.
Removal force W' depends on the return (retention) angle α': W' = P·(μ+tanα')/(1−μ·tanα'). Increasing α' raises W' sharply, and once tanα' ≥ 1/μ the denominator becomes zero or negative, giving a self-locking (permanent) joint. For μ=0.3 this happens above α' ≈ 73°. For parts you open repeatedly, keep α' around 45° so that W' is only slightly larger than the insertion force.

Real-World Applications

Consumer-electronics housings: Remote-control battery covers, router and set-top-box lids, connector locking tabs — snap-fits fix parts without screws and cut assembly cost and time. For a battery cover opened many times, a modest return angle α' makes it easy to remove; for an internal PCB clip, α' = 90° means "do not open except for service".

Automotive interior parts: Door trims, instrument panels and pillar garnishes are each held by a dozen or more snap-fit hooks. The insertion force of each hook must be kept low so the assembly-line operator is not overloaded, so designers use long, thin, low-strain beams and reach the total holding force through the number of hooks.

Household goods, toys and packaging: Flip-top cosmetic caps, building-block toy joints, storage-case lids — products that open and close repeatedly suffer fatigue. The allowable strain differs greatly between "single assembly" and "repeated use"; for repeated use, aim for less than half the single-assembly value. Tough materials such as POM and PP are favoured here.

Pre-study for CAE analysis: Before running a detailed non-linear FEM analysis, a beam-theory estimate like this tool gives a first read on "how many times the allowable strain" the design is at. If the estimate is far off, the shape can be revised before investing in mesh and material models. Conversely, if the FEM result differs from this estimate by an order of magnitude, it is a sanity check that points to a boundary-condition or contact-setup mistake.

Common Misconceptions and Pitfalls

The biggest pitfall is calculating strain while ignoring the root fillet (radius). The formula ε = 3hy/(2L²) used here is for an ideal beam of constant section and assumes the root is a right angle or a smooth radius. On a real moulded part, making the root radius too small creates a stress concentration there, and the local strain can be 1.5 to 3 times the calculated value. Almost all snap-fit failures start at the root radius. Even with a calculated safety factor of 2, a small radius leaves you with essentially no margin. Aim for a root radius of about 0.5 times the thickness h, and always round it.

Next, assuming the allowable strain ε_perm is a single fixed number. The preset values in this tool are representative figures for room temperature and a single assembly. The real ε_perm varies strongly with temperature (brittle when cold), strain rate (more brittle the faster you insert), number of cycles, glass-fiber content and the position of weld lines (where resin flows merge). In particular, when a weld line falls on the tension side of the root, the allowable strain can drop to less than half. Always check the gate position and resin flow during design.

Finally, "low insertion force = good design" is not true. Focusing only on lowering insertion force W reduces the deflection force P and therefore the retention force as well. A snap-fit is a tug-of-war between "ease of assembly (W)" and "resistance to separation (W' / retention)". And a permanent joint made self-locking with a steep return angle hurts disassembly for recycling. Driven by environmental concerns, designs that deliberately keep retention to a "can be disassembled with a tool" level are increasing. Decide the angles and dimensions while watching all three: insertion force, retention force and disassembly.

Standards & Assumptions

Standard / reference: Cantilever snap-fit design guides (BASF Snap-Fit Design Manual and equivalent material-supplier guides). Constant rectangular section: max strain \(\varepsilon = 1.5\,h\,y/L^2\), deflection force \(P = 3EIy/L^3\) with \(I = bh^3/12\), mating force \(W = P(\mu+\tan\alpha)/(1-\mu\tan\alpha)\).

Model assumptions: Linear-elastic, constant (untapered) cross-section, strain evaluated at the root. The permissible strain \(\varepsilon_\text{perm}\) is the single-assembly material value. Mating force follows from friction coefficient µ and insertion/retention angle α.

Scope & limits: ABS defaults (\(E{=}2300\,\text{MPa}, \varepsilon_\text{perm}{=}2.0\%, L{=}20, h{=}2, b{=}5, y{=}1.5\,\text{mm}\)) give \(\varepsilon{=}1.12\%\), \(P{=}4.31\,\text{N}\), insertion force 4.58 N. A tapered beam permits larger strain via the BASF deflection-magnification factor Q; this tool uses the constant-section (conservative) model. Cyclic-mating fatigue, creep and temperature dependence are out of scope.

How to Use

  1. Select the resin from the material preset (matSel); Young's modulus E and permissible strain ε_perm are set automatically (e.g. POM = 2.8 GPa / 6%, PC = 2.35 GPa / 4%, ABS = 2.3 GPa / 2%).
  2. Enter the hook geometry: beam length L (lNum, mm), root thickness h (hNum, mm), and width b (bNum, mm).
  3. Set the undercut (engagement) depth y (yNum/yRange, mm) — the deflection the hook must undergo during assembly.
  4. Adjust friction coefficient μ and the insertion/retention angles α and α'; the tool updates maximum strain ε, allowable undercut y_perm, strain safety factor, deflection force P, insertion force W, and removal force W' in real time.

Worked Example

For a polycarbonate snap-fit hook (E=2,350 MPa, ε_perm=4%): length L=12 mm, root thickness h=1.2 mm, width b=5 mm, undercut y=1.5 mm. The tool computes maximum strain ε=3hy/2L²=1.88%, allowable undercut y_perm=3.2 mm, and strain safety factor 2.13. The deflection force is P=3EIy/L³≈4.4 N; with friction coefficient μ=0.30 and lead angle α=30°, the insertion force is W=P(μ+tanα)/(1−μ·tanα)≈4.7 N, and with retention angle α'=45° the removal force is W'≈8.2 N, keeping the joint secure in service.

Practical Notes

  1. Acetal copolymer (Delrin) tolerates higher strain cycles (50,000+) versus polycarbonate (10,000) before stress-whitening; adjust y_perm downward for high-cycle medical or automotive connectors.
  2. Insertion force W must not exceed grip torque limits of assembly equipment; if W exceeds 15 N, increase root thickness h or reduce undercut depth b.
  3. Account for temperature creep in thermoplastics; allowable undercut y_perm shrinks 10–15% when operating at 60 °C versus 23 °C reference.

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